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Journal articles on the topic 'Semi-Lagrangian scheme'

Author: Grafiati

Published: 22 February 2023

Last updated: 31 July 2025

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1

Shashkin, Vladimir V., and Gordey S. Goyman. "Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid." Russian Journal of Numerical Analysis and Mathematical Modelling 35, no. 6 (2020): 355–66. http://dx.doi.org/10.1515/rnam-2020-0029.

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AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproducti

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2

Seaïd, Mohammed. "Semi-lagrangian integration schemes for viscous incompressible flows." Computational Methods in Applied Mathematics 2, no. 4 (2002): 392–409. http://dx.doi.org/10.2478/cmam-2002-0022.

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AbstractA new second-order accurate scheme for the computation of unsteady viscous incompressible flows is proposed. The scheme is based on the vorticity-stream function formulation along the characteristics and consists of combining the modified method of characteristics with an explicit scheme with an extended real stability interval. A comparison of the new method with the semi-Lagrangian Cranck-Nicolson and classical semi-Lagrangian Runge-Kutta schemes is presented. Numerical results are carried out on Navier-Stokes equations and this efficient second-order scheme has also made it possible

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3

Sørensen, B., E. Kaas, and U. S. Korsholm. "A mass-conserving and multi-tracer efficient transport scheme in the online integrated Enviro-HIRLAM model." Geoscientific Model Development 6, no. 4 (2013): 1029–42. http://dx.doi.org/10.5194/gmd-6-1029-2013.

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Abstract. In this paper a new advection scheme for the online coupled chemical–weather prediction model Enviro-HIRLAM is presented. The new scheme is based on the locally mass-conserving semi-Lagrangian method (LMCSL), where the original two-dimensional scheme has been extended to a fully three-dimensional version. This means that the three-dimensional semi-implicit semi-Lagrangian scheme which is currently used in Enviro-HIRLAM is largely unchanged. The HIRLAM model is a computationally efficient hydrostatic operational short-term numerical weather prediction model, which is used as the base

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Sørensen, B., E. Kaas, and U. S. Korsholm. "A mass conserving and multi-tracer efficient transport scheme in the online integrated Enviro-HIRLAM model." Geoscientific Model Development Discussions 5, no. 4 (2012): 3733–69. http://dx.doi.org/10.5194/gmdd-5-3733-2012.

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Abstract. In this paper a new advection scheme for the online coupled chemical-weather prediction model Enviro-HIRLAM is presented. The new scheme is based on the locally mass conserving semi-Lagrangian method (LMCSL), where the original two-dimensional scheme has been extended to a fully three-dimensional version. This means that the three-dimensional semi-implicit semi-Lagrangian scheme which is currently used in Enviro-HIRLAM, is largely unchanged. The HIRLAM model is a computationally efficient hydrostatic operational short term numerical weather prediction model, which is used as the base

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5

Lauritzen, Peter H., Eigil Kaas, and Bennert Machenhauer. "A Mass-Conservative Semi-Implicit Semi-Lagrangian Limited-Area Shallow-Water Model on the Sphere." Monthly Weather Review 134, no. 4 (2006): 1205–21. http://dx.doi.org/10.1175/mwr3115.1.

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Abstract A locally mass conservative shallow-water model using a two-time-level, semi-implicit, semi-Lagrangian integration scheme is presented. The momentum equations are solved with the traditional semi-Lagrangian gridpoint form. The explicit continuity equation is solved using a cell-integrated semi-Lagrangian scheme, and the semi-implicit part is designed such that the resulting elliptic equation is on the same form as for the traditional semi-Lagrangian gridpoint system. The accuracy of the model is assessed by running standard test cases adapted to a limited-area domain. The accuracy and

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6

Wu, Lang, Dazhi Zhang, Boying Wu, and Xiong Meng. "Fifth-Order Mapped Semi-Lagrangian Weighted Essentially Nonoscillatory Methods Near Certain Smooth Extrema." Journal of Applied Mathematics 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/127624.

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Fifth-order mapped semi-Lagrangian weighted essentially nonoscillatory (WENO) methods at certain smooth extrema are developed in this study. The schemes contain the mapped semi-Lagrangian finite volume (M-SL-FV) WENO 5 method and the mapped compact semi-Lagrangian finite difference (M-C-SL-FD) WENO 5 method. The weights in the more common scheme lose accuracy at certain smooth extrema. We introduce mapped weighting to handle the problem. In general, a cell average is applied to construct the M-SL-FV WENO 5 reconstruction, and the M-C-SL-FD WENO 5 interpolation scheme is proposed based on an in

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7

Hansen, A. B., J. Brandt, J. H. Christensen, and E. Kaas. "Semi-Lagrangian methods in air pollution models." Geoscientific Model Development 4, no. 2 (2011): 511–41. http://dx.doi.org/10.5194/gmd-4-511-2011.

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Abstract. Various semi-Lagrangian methods are tested with respect to advection in air pollution modeling. The aim is to find a method fulfilling as many of the desirable properties by Rasch andWilliamson (1990) and Machenhauer et al. (2008) as possible. The focus in this study is on accuracy and local mass conservation. The methods tested are, first, classical semi-Lagrangian cubic interpolation, see e.g. Durran (1999), second, semi-Lagrangian cubic cascade interpolation, by Nair et al. (2002), third, semi-Lagrangian cubic interpolation with the modified interpolation weights, Locally Mass Con

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8

Hansen, A. B., J. Brandt, J. H. Christensen, and E. Kaas. "Semi-Lagrangian methods in air pollution models." Geoscientific Model Development Discussions 3, no. 4 (2010): 2361–438. http://dx.doi.org/10.5194/gmdd-3-2361-2010.

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Abstract. Various semi-Lagrangian methods are tested with respect to advection in air pollution modeling. The aim is to find a method fulfilling as many of the desirable properties by Rasch and Williamson (1990) and Machenhauer et al. (2008) as possible. The focus in this study is on accuracy and local mass conservation. The methods tested are, first, classical semi-Lagrangian cubic interpolation, see e.g. Durran (1999), second, semi-Lagrangian cubic cascade interpolation, by Nair et al. (2002), third, semi-Lagrangian cubic interpolation with the modified interpolation weights, Locally Mass Co

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9

Lynch, Peter. "A Lagrange–Laplace Integration Scheme for Weather Prediction and Climate Modelling." Meteorology 1, no. 4 (2022): 355–76. http://dx.doi.org/10.3390/meteorology1040023.

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A time integration scheme based on semi-Lagrangian advection and Laplace transform adjustment has been implemented in a baroclinic primitive equation model. The semi-Lagrangian scheme makes it possible to use large time steps. However, errors arising from the semi-implicit scheme increase with the time step size. In contrast, the errors using the Laplace transform adjustment remain relatively small for typical time steps used with semi-Lagrangian advection. Numerical experiments confirm the superior performance of the Laplace transform scheme relative to the semi-implicit reference model. The

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10

Shaydurov, Vladimir V., and Viktoriya S. Petrakova. "Semi-Lagrangian approximations of the transfer operator in divergent form." Russian Journal of Numerical Analysis and Mathematical Modelling 39, no. 3 (2024): 157–64. http://dx.doi.org/10.1515/rnam-2024-0015.

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Abstract The paper demonstrates two approaches to constructing monotonic difference schemes for the transfer equation in divergent form from the family of semi-Lagrangian methods: Eulerian–Lagrangian and Lagrangian–Eulerian. Within each approach, a monotonic conservative difference scheme is proposed. It is shown that within the framework of the Lagrangian–Eulerian approach, based on the use of curvilinear grids formed by the characteristics of the approximated transfer operator, it is possible to construct monotonic difference schemes of second order accuracy.

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11

Mehrenberger, Michel, and Eric Violard. "A Hermite-Type Adaptive Semi-Lagrangian Scheme." International Journal of Applied Mathematics and Computer Science 17, no. 3 (2007): 329–34. http://dx.doi.org/10.2478/v10006-007-0027-y.

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A Hermite-Type Adaptive Semi-Lagrangian SchemeWe study a new Hermite-type interpolating operator arising in a semi-Lagrangian scheme for solving the Vlasov equation in the 2D phase space. Numerical results on uniform and adaptive grids are shown and compared with the biquadratic Lagrange interpolation introduced in (Campos Pinto and Mehrenberger, 2004) in the case of a rotating Gaussian.

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12

Voitus, F., P. Termonia, and P. Bénard. "Well-Posed Lateral Boundary Conditions for Spectral Semi-Implicit Semi-Lagrangian Schemes: Tests in a One-Dimensional Model." Monthly Weather Review 137, no. 1 (2009): 315–30. http://dx.doi.org/10.1175/2008mwr2539.1.

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Abstract The aim of this paper is to investigate the feasibility of well-posed lateral boundary conditions in a Fourier spectral semi-implicit semi-Lagrangian one-dimensional model. Two aspects are analyzed: (i) the complication of designing well-posed boundary conditions for a spectral semi-implicit scheme and (ii) the implications of such a lateral boundary treatment for the semi-Lagrangian trajectory computations at the lateral boundaries. Straightforwardly imposing boundary conditions in the gridpoint-explicit part of the semi-implicit time-marching scheme leads to numerical instabilities

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13

Bermejo, Rodolfo, and Justo Conde. "A Conservative Quasi-Monotone Semi-Lagrangian Scheme." Monthly Weather Review 130, no. 2 (2002): 423–30. http://dx.doi.org/10.1175/1520-0493(2002)130<0423:acqmsl>2.0.co;2.

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14

Hansen, A. B., B. Sørensen, P. Tarning-Andersen, J. H. Christensen, J. Brandt, and E. Kaas. "The hybrid Eulerian Lagrangian numerical scheme tested with Chemistry." Geoscientific Model Development Discussions 5, no. 4 (2012): 3695–732. http://dx.doi.org/10.5194/gmdd-5-3695-2012.

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Abstract. A newly developed advection scheme, the Hybrid Eulerian Lagrangian (HEL) scheme, has been tested, including a module for atmospheric chemistry, including 58 chemical species, and compared to two other traditional advection schemes; a classical pseudospectral Eulerian method the Accurate Space Derivative (ASD) scheme and the bi-cubic semi-Lagrangian (SL) scheme using classical rotation tests. The rotation tests have been designed to test and compare the advection schemes for different spatial and temporal resolutions in different chemical conditions (rural and urban) and for different

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15

Peng, Xindong, Feng Xiao, Wataru Ohfuchi, and Hiromitsu Fuchigami. "Conservative Semi-Lagrangian Transport on a Sphere and the Impact on Vapor Advection in an Atmospheric General Circulation Model." Monthly Weather Review 133, no. 3 (2005): 504–20. http://dx.doi.org/10.1175/mwr-2869.1.

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Abstract A conservative semi-Lagrangian scheme with rational function for interpolation is implemented in spherical geometry and tested in an atmospheric general circulation model (AGCM). The new scheme, different from the conventional semi-Lagrangian method, is conservative and oscillation free. By introducing polar mixing and a time split computation of divergence, the scheme can compute advection transport correctly over the polar regions. Idealized advection tests with various velocity fields were carried out to demonstrate numerical accuracy and conservation in comparison with the spectra

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16

Henry Juang, Hann-Ming, and Song-You Hong. "Forward Semi-Lagrangian Advection with Mass Conservation and Positive Definiteness for Falling Hydrometeors." Monthly Weather Review 138, no. 5 (2010): 1778–91. http://dx.doi.org/10.1175/2009mwr3109.1.

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Abstract A semi-Lagrangian advection scheme is developed for falling hydrometeors in hopes of replacing the conventional Eulerian scheme that has been widely used in the cloud microphysics scheme of numerical atmospheric models. This semi-Lagrangian scheme uses a forward advection method to determine the advection path with or without iteration, and advected mass in a two-time-level algorithm with mass conservation. Monotonicity is considered in mass-conserving interpolation between Lagrangian grids and model Eulerian grids, thus making it a positive definite advection scheme. For mass-conserv

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17

Xiao, F., T. Okazaki, and M. Satoh. "An Accurate Semi-Lagrangian Scheme for Raindrop Sedimentation." Monthly Weather Review 131, no. 5 (2003): 974–83. http://dx.doi.org/10.1175/1520-0493(2003)131<0974:aassfr>2.0.co;2.

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18

Sun, Wen-Yih, and Ming-Teh Sun. "Mass Correction Applied to Semi-Lagrangian Advection Scheme." Monthly Weather Review 132, no. 4 (2004): 975–84. http://dx.doi.org/10.1175/1520-0493(2004)132<0975:mcatsa>2.0.co;2.

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19

Nair, Ramachandran D., Jeffrey S. Scroggs, and Frederick H. M. Semazzi. "A forward-trajectory global semi-Lagrangian transport scheme." Journal of Computational Physics 190, no. 1 (2003): 275–94. http://dx.doi.org/10.1016/s0021-9991(03)00274-2.

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20

Lee, H. N. "A Semi-Lagrangian Transport Scheme with Spectral Interpolation." Journal of Applied Meteorology 32, no. 12 (1993): 1908–18. http://dx.doi.org/10.1175/1520-0450(1993)032<1908:asltsw>2.0.co;2.

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21

Cotter, C. J., J. Frank, and S. Reich. "The remapped particle-mesh semi-Lagrangian advection scheme." Quarterly Journal of the Royal Meteorological Society 133, no. 622 (2007): 251–60. http://dx.doi.org/10.1002/qj.11.

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22

Sun, Wen-Yih, Kao-San Yeh, and Rueen-Yuh Sun. "A simple semi-Lagrangian scheme for advection equations." Quarterly Journal of the Royal Meteorological Society 122, no. 533 (1996): 1211–26. http://dx.doi.org/10.1002/qj.49712253310.

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23

Degawa, Tomohiro, and Tomomi Uchiyama. "Improvements to the convection scheme in the vortex particle method using a semi-Lagrangian method." Journal of Algorithms & Computational Technology 12, no. 3 (2018): 223–33. http://dx.doi.org/10.1177/1748301818771811.

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This study focuses on the convection scheme in the vortex particle method. The usual two-step convection procedure for vortex elements, which comprises the convection of vortex elements on each grid point and redistribution of vorticity into each grid point, is extremely difficult to parallelize because of unavoidable memory-write conflictions in the redistribution step, thereby limiting the computational speed. We apply a semi-Lagrangian method called the cubic semi-Lagrangian method, as the convection scheme in the vortex particle method to improve space–time accuracy and accelerate computat

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24

McDonald, A. "A Semi-Lagrangian and Semi-Implicit Two Time-Level Integration Scheme." Monthly Weather Review 114, no. 5 (1986): 824–30. http://dx.doi.org/10.1175/1520-0493(1986)114<0824:aslasi>2.0.co;2.

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25

Mohammadian, A., and D. Y. Le Roux. "Conservative semi-implicit semi-Lagrangian scheme for simulation of shallow flows." Computer Physics Communications 174, no. 2 (2006): 99–108. http://dx.doi.org/10.1016/j.cpc.2005.08.007.

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26

Temperton, Clive, and Andrew Staniforth. "An Efficient Two-Time-Level Semi-Lagrangian Semi-Implicit Integration Scheme." Quarterly Journal of the Royal Meteorological Society 113, no. 477 (1987): 1025–39. http://dx.doi.org/10.1002/qj.49711347714.

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27

Charlesworth, Edward J., Ann-Kristin Dugstad, Frauke Fritsch, Patrick Jöckel, and Felix Plöger. "Impact of Lagrangian transport on lower-stratospheric transport timescales in a climate model." Atmospheric Chemistry and Physics 20, no. 23 (2020): 15227–45. http://dx.doi.org/10.5194/acp-20-15227-2020.

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Abstract. We investigate the impact of model trace gas transport schemes on the representation of transport processes in the upper troposphere and lower stratosphere. Towards this end, the Chemical Lagrangian Model of the Stratosphere (CLaMS) was coupled to the ECHAM/MESSy Atmospheric Chemistry (EMAC) model and results from the two transport schemes (Lagrangian critical Lyapunov scheme and flux-form semi-Lagrangian, respectively) were compared. Advection in CLaMS was driven by the EMAC simulation winds, and thereby the only differences in transport between the two sets of results were caused b

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28

Qiu, Jing-Mei, and Chi-Wang Shu. "Conservative Semi-Lagrangian Finite Difference WENO Formulations with Applications to the Vlasov Equation." Communications in Computational Physics 10, no. 4 (2011): 979–1000. http://dx.doi.org/10.4208/cicp.180210.251110a.

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AbstractIn this paper, we propose a new conservative semi-Lagrangian (SL) finite difference (FD) WENO scheme for linear advection equations, which can serve as a base scheme for the Vlasov equation by Strang splitting [4]. The reconstruction procedure in the proposed SL FD scheme is the same as the one used in the SL finite volume (FV) WENO scheme [3]. However, instead of inputting cell averages and approximate the integral form of the equation in a FV scheme, we input point values and approximate the differential form of equation in a FD spirit, yet retaining very high order (fifth order in o

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29

Norman, Matthew R., and Ramachandran D. Nair. "Inherently Conservative Nonpolynomial-Based Remapping Schemes: Application to Semi-Lagrangian Transport." Monthly Weather Review 136, no. 12 (2008): 5044–61. http://dx.doi.org/10.1175/2008mwr2499.1.

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Abstract A group of new conservative remapping schemes based on nonpolynomial approximations is proposed. The remapping schemes rely on the conservative cascade scheme (CCS), which employs an efficient sequence of 1D remapping operations to solve a multidimensional problem. The present study adapts three new nonpolynomial-based reconstructions of subgrid variation to the CCS: the Piecewise Hyperbolic Method (PHM), the Piecewise Double Hyperbolic Method (PDHM), and the Piecewise Rational Method (PRM) for comparison with the baseline method: the Piecewise Parabolic Method (PPM). Additionally, an

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30

Kar, Sajal K. "An Explicit Time-Difference Scheme with an Adams–Bashforth Predictor and a Trapezoidal Corrector." Monthly Weather Review 140, no. 1 (2012): 307–22. http://dx.doi.org/10.1175/mwr-d-10-05066.1.

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Abstract A new predictor-corrector time-difference scheme that employs a second-order Adams–Bashforth scheme for the predictor and a trapezoidal scheme for the corrector is introduced. The von Neumann stability properties of the proposed Adams–Bashforth trapezoidal scheme are determined for the oscillation and friction equations. Effectiveness of the scheme is demonstrated through a number of time integrations using finite-difference numerical models of varying complexities in one and two spatial dimensions. The proposed scheme has useful implications for the fully implicit schemes currently e

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31

Hoppe, C. M., L. Hoffmann, P. Konopka, et al. "The implementation of the CLaMS Lagrangian transport core into the chemistry climate model EMAC 2.40.1: application on age of air and transport of long-lived trace species." Geoscientific Model Development 7, no. 6 (2014): 2639–51. http://dx.doi.org/10.5194/gmd-7-2639-2014.

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Abstract. Lagrangian transport schemes have proven to be useful tools for modelling stratospheric trace gas transport since they are less diffusive than classical Eulerian schemes and therefore especially well suited for maintaining steep tracer gradients. Here, we present the implementation of the full-Lagrangian transport core of the Chemical Lagrangian Model of the Stratosphere (CLaMS) into the ECHAM/MESSy Atmospheric Chemistry model (EMAC). We performed a 10-year time-slice simulation to evaluate the coupled model system EMAC/CLaMS. Simulated zonal mean age of air distributions are compare

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Hoppe, C. M., L. Hoffmann, P. Konopka, et al. "The implementation of the CLaMS Lagrangian transport core into the chemistry climate model EMAC 2.40.1: application on age of air and transport of long-lived trace species." Geoscientific Model Development Discussions 7, no. 2 (2014): 1759–90. http://dx.doi.org/10.5194/gmdd-7-1759-2014.

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Abstract. Lagrangian transport schemes have proven to be useful tools for modelling stratospheric trace gas transport since they are less diffusive than classical Eulerian schemes and therefore especially well suited for maintaining steep tracer gradients. Here, we present the implementation of the full-Lagrangian transport core of the Chemical Lagrangian Model of the Stratosphere (CLaMS) into the ECHAM/MESSy Atmospheric Chemistry model (EMAC). We performed a ten-year time-slice simulation to evaluate the coupled model system EMAC/CLaMS. Simulated zonal mean age of air distributions are compar

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33

Tang, Jie, Chungang Chen, Xueshun Shen, Feng Xiao, and Xingliang Li. "A Positivity-preserving Conservative Semi-Lagrangian Multi-moment Global Transport Model on the Cubed Sphere." Advances in Atmospheric Sciences 38, no. 9 (2021): 1460–73. http://dx.doi.org/10.1007/s00376-021-0393-7.

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AbstractA positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. Two kinds of moments (i.e., point values (PV moment) at cell interfaces and volume integrated average (VIA moment) value) are defined within a single cell. The PV moment is updated by a conventional semi-Lagrangian method, while the VIA moment is cast by the flux form formulation to assure the exact numerical conservation. Different from the spatial approximation used in the CSL2 (conservative semi-Lagrangian scheme with second order pol

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Ritchie, Harold. "Eliminating the Interpolation Associated with the Semi-Lagrangian Scheme." Monthly Weather Review 114, no. 1 (1986): 135–46. http://dx.doi.org/10.1175/1520-0493(1986)114<0135:etiawt>2.0.co;2.

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Becerra-Sagredo, Julián, Carlos Málaga, and Francisco Mandujano. "Moments Preserving and high-resolution Semi-Lagrangian Advection Scheme." SIAM Journal on Scientific Computing 38, no. 4 (2016): A2141—A2161. http://dx.doi.org/10.1137/140990619.

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36

Böttcher, Michael. "A Semi-Lagrangian Advection Scheme with Modified Exponential Splines." Monthly Weather Review 124, no. 4 (1996): 716–29. http://dx.doi.org/10.1175/1520-0493(1996)124<0716:aslasw>2.0.co;2.

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Behrens, Jörn. "An Adaptive Semi-Lagrangian Advection Scheme and Its Parallelization." Monthly Weather Review 124, no. 10 (1996): 2386–95. http://dx.doi.org/10.1175/1520-0493(1996)124<2386:aaslas>2.0.co;2.

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38

Takizawa, K., T. Yabe, and T. Nakamura. "Multi-dimensional semi-Lagrangian scheme that guarantees exact conservation." Computer Physics Communications 148, no. 2 (2002): 137–59. http://dx.doi.org/10.1016/s0010-4655(02)00472-1.

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Bermejo, R., and J. Carpio. "A semi-Lagrangian-Galerkin projection scheme for convection equations." IMA Journal of Numerical Analysis 30, no. 3 (2009): 799–831. http://dx.doi.org/10.1093/imanum/drn044.

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40

Carlini, E., and F. J. Silva. "A Semi-Lagrangian scheme for the Fokker-Planck equation." IFAC-PapersOnLine 49, no. 8 (2016): 272–77. http://dx.doi.org/10.1016/j.ifacol.2016.07.453.

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41

Sun, Wen-Yih, and Kao-San Yeh. "A general semi-lagrangian advection scheme employing forward trajectories." Quarterly Journal of the Royal Meteorological Society 123, no. 544 (1997): 2463–76. http://dx.doi.org/10.1002/qj.49712354415.

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42

Côté, Jean, and Andrew Staniforth. "A Two-Time-Level Semi-Lagrangian Semi-implicit Scheme for Spectral Models." Monthly Weather Review 116, no. 10 (1988): 2003–12. http://dx.doi.org/10.1175/1520-0493(1988)116<2003:attlsl>2.0.co;2.

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43

Bourchtein, Andrei. "Semi-Lagrangian semi-implicit locally one-dimensional scheme for hydrostatic atmospheric model." Mathematics and Computers in Simulation 73, no. 1-4 (2006): 38–51. http://dx.doi.org/10.1016/j.matcom.2006.06.006.

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44

Bourchtein, A., and L. Bourchtein. "Semi-Lagrangian semi-implicit time-splitting scheme for the shallow water equations." International Journal for Numerical Methods in Fluids 54, no. 4 (2007): 453–71. http://dx.doi.org/10.1002/fld.1410.

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45

Wong, May, William C. Skamarock, Peter H. Lauritzen, and Roland B. Stull. "A Cell-Integrated Semi-Lagrangian Semi-Implicit Shallow-Water Model (CSLAM-SW) with Conservative and Consistent Transport." Monthly Weather Review 141, no. 7 (2013): 2545–60. http://dx.doi.org/10.1175/mwr-d-12-00275.1.

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Abstract A Cartesian semi-implicit solver using the Conservative Semi-Lagrangian Multitracer (CSLAM) transport scheme is constructed and tested for shallow-water (SW) flows. The SW equations solver (CSLAM-SW) uses a discrete semi-implicit continuity equation specifically designed to ensure a conservative and consistent transport of constituents by avoiding the use of a constant mean reference state. The algorithm is constructed to be similar to typical conservative semi-Lagrangian semi-implicit schemes, requiring at each time step a single linear Helmholtz equation solution and a single applic

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Kaas, E., B. Sørensen, P. H. Lauritzen, and A. B. Hansen. "A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics." Geoscientific Model Development 6, no. 6 (2013): 2023–47. http://dx.doi.org/10.5194/gmd-6-2023-2013.

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Abstract. A new hybrid Eulerian–Lagrangian numerical scheme (HEL) for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is int

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Kaas, E., B. Sørensen, P. H. Lauritzen, and A. B. Hansen. "A hybrid Eulerian Lagrangian numerical scheme for solving prognostic equations in fluid dynamics." Geoscientific Model Development Discussions 6, no. 3 (2013): 3819–91. http://dx.doi.org/10.5194/gmdd-6-3819-2013.

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Abstract. A new hybrid Eulerian Lagrangian numerical scheme (HEL) for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is int

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Wong, May, William C. Skamarock, Peter H. Lauritzen, Joseph B. Klemp, and Roland B. Stull. "Testing of a Cell-Integrated Semi-Lagrangian Semi-Implicit Nonhydrostatic Atmospheric Solver (CSLAM-NH) with Idealized Orography." Monthly Weather Review 143, no. 4 (2015): 1382–98. http://dx.doi.org/10.1175/mwr-d-14-00059.1.

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Abstract A recently developed cell-integrated semi-Lagrangian (CISL) semi-implicit nonhydrostatic atmospheric solver that uses the conservative semi-Lagrangian multitracer (CSLAM) transport scheme is extended to include orographic influences. With the introduction of a new semi-implicit CISL discretization of the continuity equation, the nonhydrostatic solver, called CSLAM-NH, has been shown to ensure inherently conservative and numerically consistent transport of air mass and other scalar variables, such as moisture and passive tracers. The extended CSLAM-NH presented here includes two main m

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Kaas, Eigil, and Joakim R. Nielsen. "A Mass-Conserving Quasi-Monotonic Filter for Use in Semi-Lagrangian Models." Monthly Weather Review 138, no. 5 (2010): 1858–76. http://dx.doi.org/10.1175/2009mwr3173.1.

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Abstract A new mass-conserving and quasi-monotonic antidiffusive filter has been designed for application in semi-Lagrangian-type models. The filter redistributes local mass such that the resulting values are brought closer to target values. The target values, in turn, are specified from a nonlinear antidiffusion of the original nonfiltered forecast. To achieve quasi-monotonicity, the target values are constrained to a certain interval, defined by the minimum and maximum value of the upstream grid cells surrounding the semi-Lagrangian departure point. Allowing a less local reorganization of ma

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Lauritzen, Peter Hjort, Mark A. Taylor, James Overfelt, et al. "CAM-SE–CSLAM: Consistent Coupling of a Conservative Semi-Lagrangian Finite-Volume Method with Spectral Element Dynamics." Monthly Weather Review 145, no. 3 (2017): 833–55. http://dx.doi.org/10.1175/mwr-d-16-0258.1.

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An algorithm to consistently couple a conservative semi-Lagrangian finite-volume transport scheme with a spectral element (SE) dynamical core is presented. The semi-Lagrangian finite-volume scheme is the Conservative Semi-Lagrangian Multitracer (CSLAM), and the SE dynamical core is the National Center for Atmospheric Research (NCAR)’s Community Atmosphere Model–Spectral Elements (CAM-SE). The primary motivation for coupling CSLAM with CAM-SE is to accelerate tracer transport for multitracer applications. The coupling algorithm result is an inherently mass-conservative, shape-preserving, and co

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